United signed Cavani, 33, on deadline day eight months after Ighalo, 32, joined on a deadline day loan from Shanghai Shenhua.
Ighalo made a superb start for United, scoring five in his first four starts before the lockdown, yet the Nigerian has seldom impressed since European football restarted in June.
United extended Ighalo’s loan until January 31 but he has become marginalised by the presence of Cavani, who began training with his new teammates on Sunday after a period of quarantine.
Cavani has not travelled to France for the Champions League group stage opener against former club Paris Saint-Germain and Ighalo – back on the bench for United at Newcastle – is expected to be named as a substitute at the Parc des Princes.
“I think as a team and a club we always want to get players in,” Solskjaer said. “And I think Edinson coming in, we’ll give him time to adapt to the Premier League and get his sharpness and fitness back.
“We’ve had some very good performances by Odion and he’s still a very important part of this squad.”
Ighalo’s only starts for United this season were in the Carabao Cup wins over Luton Town and Brighton and he has not scored since the FA Cup quarter-final victory over Norwich in June.
United can name 12 substitutes in Champions League games and Ighalo is guaranteed a matchday squad berth at PSG, with Mason Greenwood and Jesse Lingard also out.